Method for generating three-dimensional mesh method for magnetic field of rotating machine, system for generating three-dimensional mesh, system for analyzing magnetic field of rotating machine, computer program, and recording medium

ABSTRACT

Based on rectangular element data constituting a boundary surface that separates a rotating machine into a stator-side portion and a rotor-side portion, and polygonal or polyhedral element data constituting the stator-side portion and the rotor-side portion excluding the boundary surface, tetrahedral elements including nodes of each of the stator-side portion and the rotor-side portion are created, a node is created at an arbitrary distance from the gravity of the rectangular element in a normal direction for each of the rectangular elements on the boundary surface, mesh division is performed for the tetrahedral elements based on the node at the arbitrary distance and nodes on the boundary surface, and mesh division is further performed based on nodes of the stator and the rotor.

This application is the national phase under 35 U.S.C. § 371 of PCTInternational Application No. PCT/JP02/12572 which has an Internationalfiling date of Nov. 29, 2002 and designated the United States ofAmerica.

TECHNICAL FIELD

The present invention relates to a method of generating athree-dimensional mesh of a rotating machine including a spatial area,for the analysis of electromagnetic field using a finite element method;a three-dimensional mesh generator for use in implementing the method; acomputer program for realizing a computer as the three-dimensional meshgenerator; a computer-readable memory product storing the computerprogram; a method for analyzing magnetic field of a rotating machine byusing a three-dimensional mesh; a magnetic field analyzer for use inimplementing the method; a computer program for realizing a computer asthe magnetic field analyzer; and a computer-readable memory productstoring the computer program.

BACKGROUND ART

For the analysis of the structure of a three-dimensional object, afinite element method is mainly used. In the finite element method, athree-dimensional object is expressed by a combination of a plurality ofpolyhedral elements, and numerical analysis is performed by definingthat the respective elements are joined at a finite number of nodesconstituting the elements. The operation of dividing a three-dimensionalobject into a plurality of elements is called mesh division, and adivided mesh of a three-dimensional model to be analyzed is defined bymesh data composed of information about the positions of nodes, etc.

In an electromagnetic field analysis using the finite element methodthat takes a rotational motion into consideration, a three-dimensionalmesh of a rotating machine such as a motor is generated by the followingmethod. In a spatial area between a stator and a rotor, a boundarysurface for separating the rotating machine and the spatial area into astator-side portion and a rotor-side portion is set, and two-dimensionalmeshes of the stator-side portion and the rotor-side portion aregenerated on a cross section perpendicular to a rotation axis direction.The generated two-dimensional mesh is extended in the rotation axisdirection to generate a three-dimensional mesh of an analysis areacomposed of the rotating machine and the spatial area. By shifting thethree-dimensional mesh of the rotor-side portion from the boundarysurface by an amount of one element with respect to the stator-sideportion, it is possible to rotate the rotor, and thus it is possible toperform a magnetic field analysis of the rotating machine while rotatingthe rotor.

Moreover, by generating a three-dimensional mesh of the entire rotatingmachine including the spatial area every time the rotor is rotated, itis also possible to perform a magnetic field analysis of the rotatingmachine while rotating the rotor.

With the above-described method of generating a three-dimensional meshby extending a two-dimensional mesh, it is possible to express the shapeof a rotating machine having a simple shape by the generatedthree-dimensional mesh. However, for a crow-pole type rotating machineor a rotating machine with a coil end having a complicated shape, it isimpossible to generate a three-dimensional mesh showing the structure ofthe rotating machine by extending a two-dimensional mesh since the shapeof the rotating machine is not uniform on the cross sectionsperpendicular to the rotation axis.

On the other hand, with the above-described method of generating athree-dimensional mesh of the entire rotating machine every time therotor is rotated, it is possible to generate a three-dimensional mesh ofa rotating machine having a complicated shape, but it is necessary toregenerate a three-dimensional mesh every time the rotor is rotated, andtherefore this method has the problem that it requires enormouscalculation time for the analysis.

DISCLOSURE OF THE INVENTION

The present invention has been made with the aim of solving the aboveproblems, and it is an object of the present invention to provide athree-dimensional mesh generation method capable of generating athree-dimensional mesh suitable for a magnetic field analysis of arotating machine having a complicated shape by generatingthree-dimensional meshes of a stator-side portion and a rotor-sideportion by using data of quadrilateral elements into which a boundarysurface separating the rotating machine into the stator-side portion andthe rotor-side portion is divided; a three-dimensional mesh generatorfor use in implementing the method; a computer program for realizing acomputer as the three-dimensional mesh generator; a computer-readablememory product storing the computer program; a method of analyzingmagnetic field of the rotating machine in a short calculation time byrotating the three-dimensional mesh of the rotor-side portion from theboundary surface; a magnetic field analyzer for use in implementing themethod; a computer program for realizing a computer as the magneticfield analyzer; and a computer-readable memory product storing thecomputer program.

A three-dimensional mesh generation method according to a first aspectof the invention is a method of generating three-dimensional meshes of astator-side portion and a rotor-side portion of a rotating machinecomposed of a stator and a rotor by setting a boundary surface in aspatial area between the stator and the rotor to separate the rotatingmachine and the spatial area into the stator-side portion and therotor-side portion, prescribing shapes of the stator-side portion andthe rotor-side portion, and dividing each of the stator-side portion andthe rotor-side portion into polyhedral elements or polygonal elements,and characterized by comprising: dividing the boundary surface intoquadrilateral elements; creating tetrahedral elements including nodes ofeach of the stator-side portion and the rotor-side portion; creating apoint at an arbitrary distance from a gravity of the quadrilateralelement in a normal direction for each of the quadrilateral elementsconstituting the boundary surface; performing mesh division for thetetrahedral elements based on the point at the arbitrary distance andnodes on the boundary surface; and further performing mesh divisionbased on nodes of the stator and the rotor to generate three-dimensionalmeshes.

A three-dimensional mesh generation method according to a second aspectof the invention is a method of generating a three-dimensional mesh of arotating machine including a spatial area between a stator and a rotor,and characterized by comprising: setting a boundary surface in thespatial area to separate the rotating machine and the spatial area intoa stator-side portion and a rotor-side portion; prescribing shapes ofthe stator-side portion and the rotor-side portion; dividing theboundary surface into quadrilateral elements; dividing the stator-sideportion and the rotor-side portion excluding the boundary surface intopolyhedral elements or polygonal elements; creating tetrahedral elementsincluding nodes of each of the stator-side portion and the rotor-sideportion; creating a point at an arbitrary distance from a gravity of thequadrilateral element in a normal direction for each of thequadrilateral elements constituting the boundary surface; performingmesh division for the tetrahedral elements based on the point at thearbitrary distance and nodes on the boundary surface; and furtherperforming mesh division based on nodes of the stator and the rotor togenerate three-dimensional meshes.

A three-dimensional mesh generation method according to a third aspectof the invention is based on the first or second aspect of theinvention, and characterized in that the mesh division is performedusing the Delaunay method.

A magnetic field analysis method for a rotating machine according to afourth aspect of the invention is a method of performing a magneticfield analysis of a rotating machine by a finite element method using athree-dimensional mesh of the rotating machine including a spatial areabetween a stator and a rotor, and characterized by comprising:generating a three-dimensional mesh of a rotating machine to be analyzedby using the three-dimensional mesh generation method of any one of thefirst through third aspects of the invention; and rotating thethree-dimensional mesh of the rotor-side portion by shifting theelements from the boundary surface, and performing a magnetic fieldanalysis by the finite element method.

A three-dimensional mesh generator according to a fifth aspect of theinvention is a three-dimensional mesh generator for generatingthree-dimensional meshes of a stator-side portion and a rotor-sideportion of a rotating machine composed of a stator and a rotor based onelement data generated by setting a boundary surface in a spatial areabetween the stator and the rotor to separate the rotating machine andthe spatial area into the stator-side portion and the rotor-sideportion, prescribing shapes of the stator-side portion and therotor-side portion, dividing the boundary surface into quadrilateralelements, and dividing each of the stator-side portion and therotor-side portion excluding the boundary surface into polyhedralelements or polygonal elements, and characterized by comprising: meansfor creating tetrahedral elements including nodes of each of thestator-side portion and the rotor-side portion; means for creating apoint at an arbitrary distance from a gravity of the quadrilateralelement in a normal direction for each of the quadrilateral elementsconstituting the boundary surface; first dividing means for performingmesh division for the tetrahedral elements based on the point at thearbitrary distance and nodes on the boundary surface; and seconddividing means for further performing mesh division based on nodes ofthe stator and the rotor.

A three-dimensional mesh generator according to a sixth aspect of theinvention is based on the fifth aspect of the invention, andcharacterized in that the first dividing means and the second dividingmeans perform mesh division using the Delaunay method.

A magnetic field analyzer for a rotating machine according to a seventhaspect of the invention is an apparatus for performing a magnetic fieldanalysis of a rotating machine by a finite element method using athree-dimensional mesh of the rotating machine including a spatial areabetween a stator and a rotor, and characterized by comprising: means forgenerating a three-dimensional mesh of a rotating machine to be analyzedby using the three-dimensional mesh generator of the fifth or sixthaspect of the invention; and means for rotating the three-dimensionalmesh of the rotor-side portion by shifting the elements from theboundary surface, and performing a magnetic field analysis by the finiteelement method.

A computer program according to an eighth aspect of the invention is acomputer program for causing a computer to generate three-dimensionalmeshes of a stator-side portion and a rotor-side portion of a rotatingmachine composed of a stator and a rotor by using element data generatedby setting a boundary surface in a spatial area between the stator andthe rotor to separate the rotating machine and the spatial area into thestator-side portion and the rotor-side portion, prescribing shapes ofthe stator-side portion and the rotor-side portion, dividing theboundary surface into quadrilateral elements, and dividing each of thestator-side portion and the rotor-side portion into polyhedral elementsor polygonal elements, and characterized by causing a computer toexecute the steps of creating tetrahedral elements including nodes ofeach of the stator-side portion and the rotor-side portion; creating apoint at an arbitrary distance from a gravity of the quadrilateralelement in a normal direction for each of the quadrilateral elementsconstituting the boundary surface; performing mesh division for thetetrahedral elements based on the point at the arbitrary distance andnodes on the boundary surface; and further performing mesh divisionbased on nodes of the stator and the rotor to generate three-dimensionalmeshes.

A computer program according to a ninth aspect of the invention is acomputer program for causing a computer to perform a magnetic fieldanalysis of a rotating machine by a finite element method using athree-dimensional mesh of the rotating machine including a spatial areabetween a stator and a rotor, and characterized by causing a computer toexecute the steps of: generating a three-dimensional mesh of a rotatingmachine to be analyzed by using the computer program of the eighthaspect of the invention; and rotating the three-dimensional mesh of therotor-side portion by shifting the elements from the boundary surface,and performing a magnetic field analysis by the finite element method.

A computer-readable memory product according to a tenth aspect of theinvention is a memory product readable by a computer and storing acomputer program for causing a computer to generate three-dimensionalmeshes of a stator-side portion and a rotor-side portion of a rotatingmachine composed of a stator and a rotor by using element data generatedby setting a boundary surface in a spatial area between the stator andthe rotor to separate the rotating machine and the spatial area into thestator-side portion and the rotor-side portion, prescribing shapes ofthe stator-side portion and the rotor-side portion, dividing theboundary surface into quadrilateral elements, and dividing each of thestator-side portion and the rotor-side portion into polyhedral elementsor polygonal elements, and characterized by storing a computer programfor causing a computer to execute the steps of creating tetrahedralelements including nodes of each of the stator-side portion and therotor-side portion; creating a point at an arbitrary distance from agravity of the quadrilateral element in a normal direction for each ofthe quadrilateral elements constituting the boundary surface; performingmesh division for the tetrahedral elements based on the point at thearbitrary distance and nodes on the boundary surface; and furtherperforming mesh division based on nodes of the stator and the rotor togenerate three-dimensional meshes.

A computer-readable memory product according to an eleventh aspect ofthe invention is a memory product readable by a computer and storing acomputer program for causing a computer to perform a magnetic fieldanalysis of a rotating machine by a finite element method using athree-dimensional mesh of the rotating machine including a spatial areabetween a stator and a rotor, and characterized by storing a computerprogram for causing a computer to execute the steps of: generating athree-dimensional mesh of a rotating machine to be analyzed by using thememory product of the tenth aspect of the invention; and rotating thethree-dimensional mesh of the rotor-side portion by shifting theelements from the boundary surface, and performing a magnetic fieldanalysis by the finite element method.

In the first, second, fifth, eighth and tenth aspects of the invention,for the magnetic field analysis of a rotating machine, when generatingthree-dimensional meshes of the stator-side portion and the rotor-sideportion by setting a boundary surface in the spatial area between thestator and the rotor of the rotating machine, tetrahedral elementsincluding nodes of each of the stator-side portion and the rotor-sideportion are created based on quadrilateral element data constituting theboundary surface divided by a suitable method, and polyhedral element orpolygonal element data constituting the stator-side portion and therotor-side portion excluding the boundary surface; a point is created atan arbitrary distance from the gravity of the quadrilateral element in anormal direction for each of the quadrilateral elements constituting theboundary surface; mesh division is performed for the tetrahedralelements based on nodes on the boundary surface and the arbitrary point;and mesh division is further performed based on nodes constituting thestator and the rotor to generate three-dimensional meshes of thestator-side portion and the rotor-side portion. Accordingly, even for arotating machine whose shape is so complicated that a three-dimensionalmesh cannot be generated by the conventional three-dimensional meshgeneration method in which a two-dimensional mesh is generated on across section perpendicular to the rotation axis of the rotating machineand a three-dimensional mesh is generated by extending the generatedtwo-dimensional mesh in the rotation axis direction, it is possible togenerate three-dimensional meshes of the stator-side portion and therotor-side portion respectively, and thus it is possible to generatethree-dimensional meshes of the stator-side portion and the rotor-sideportion for a magnetic field analysis regardless of the shape of therotating machine.

In the third and sixth aspects of the invention, by performing meshdivision for the tetrahedral elements including nodes of each of thestator-side portion and the rotor-side portion by the Delaunay methodbased on nodes, it is possible to fully automatically divide thestator-side portion and the rotor-side portion into tetrahedral elementsto generate meshes.

In the fourth, seventh, ninth and eleventh aspects of the invention,since the magnetic field analysis of the rotating machine is performedby the finite element method using the generated three-dimensionalmeshes, it is possible to perform accurate magnetic field analysis in ashorter calculation time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a three-dimensional mesh generatoraccording to the present invention;

FIG. 2 is a perspective view showing an initial three-dimensional meshof a rotor-side portion;

FIG. 3 is an explanatory view showing the steps of generating a finalthree-dimensional mesh by noting one rectangular element;

FIG. 4 is a perspective view showing the final three-dimensional mesh ofthe rotor-side portion;

FIG. 5 is a flowchart explaining the processing steps performed by a CPUof the three-dimensional mesh generator of the present invention;

FIG. 6 is a block diagram showing a magnetic field analyzer for arotating machine according to the present invention; and

FIG. 7 is a flowchart showing the processing steps performed by a CPU ofthe magnetic field analyzer for a rotating machine according to thepresent invention.

BEST MODE FOR IMPLEMENTING THE INVENTION

The following description will explain the present invention withreference to the drawings illustrating an embodiment thereof.

FIG. 1 is a block diagram showing a three-dimensional mesh generatoraccording to the present invention. Reference numeral 1 is athree-dimensional mesh generator of the present invention using acomputer, which comprises: a CPU 11 for performing processing; a RAM 12;an external memory device 13 such as a CD-ROM drive; and an internalmemory device 14 such as a hard disk. By reading a computer program 20of the present invention from a memory product 2 such as a CD-ROM of thepresent invention by the external memory device 13, storing the readcomputer program 20 into the internal memory device 14 and loading thecomputer program 20 into the RAM 12, the CPU 11 executes processesnecessary for the three-dimensional mesh generator 1, based on thecomputer program 20. The three-dimensional mesh generator 1 comprises aninput device 15 such as a keyboard or a mouse, and an output device 16such as a liquid crystal display or a CRT display, and receives theuser's operations such as input of data.

Moreover, the three-dimensional mesh generator 1 may comprise acommunication interface 17, and may download the computer program 20 ofthe present invention from a server device 3 connected to thecommunication interface 17 and execute processing by the CPU 11.

Next, the following description will explain a three-dimensional meshgeneration method of the present invention by using a motor with a rotorsurrounded by a stator as a rotating machine. A boundary surface is setat a substantially center of a spatial area between the stator and therotor to separate the motor including the spatial area into astator-side portion including the stator and the spatial area positionedinside the boundary surface, and a rotor-side portion including therotor and the spatial area positioned outside the boundary surface, andthree-dimensional meshes of the stator-side portion and the rotor-sideportion are respectively generated.

A method of generating a three-dimensional mesh of the rotor-sideportion will be explained below. The user generates an initialthree-dimensional mesh of the rotor-side portion by using a suitablemethod such as CAD. First, a shape of the rotor-side portion isprescribed, and the boundary surface is divided into a predeterminednumber of rectangular elements in a grid form. Next, the rotor-sideportion excluding the boundary surface is divided into a predeterminednumber of polyhedral elements or polygonal elements. FIG. 2 is aperspective view showing the initial three-dimensional mesh of therotor-side portion. FIG. 2( a) is a perspective view showing only therotor, and FIG. 2( b) is a perspective view showing only the rotorrotated by 90 degrees from FIG. 2( a). FIG. 2( c) is a perspective viewshowing the rotor-side portion including the spatial area positionedinside the boundary surface, and FIG. 2( d) is a perspective viewshowing the rotor-side portion rotated by 90 degrees from FIG. 2( c).When the rotor-side portion excluding the boundary surface isthree-dimensionally divided, it is divided into polyhedral elements(hexahedral elements and pentahedral elements). On the other hand, whenthe rotor-side portion is two-dimensionally divided, it is divided intopolygonal elements (quadrilateral elements and triangular elements).

Next, in the three-dimensional mesh generator of the present invention,first, tetrahedral elements (super tetra) including nodes of the initialthree-dimensional mesh are created based on the initialthree-dimensional mesh data of the rotor-side portion. Thereafter, a newnode is created for each of rectangular elements constituting theboundary surface as follows. FIG. 3 is an explanatory view showing thesteps of generating a final three-dimensional mesh by noting onearbitrary rectangular element among the rectangular elementsconstituting the boundary surface. FIG. 3( a) is a perspective view ofthe rectangular element whose vertices are nodes P1, P2, P3 and P4. Asshown in FIG. 3( b), the gravity of the rectangular element iscalculated, and a point is created at an arbitrary distance H from thegravity to the rotor side in a normal direction. If this point isdenoted as a node P5, the node P5 is created for all rectangularelements constituting the boundary surface.

Next, mesh division is performed for super tetra by the Delaunay methodbased on the nodes (P1, P2, P3, and P4) and the node P5 of allrectangular elements. Since the three-dimensional space is divided intotetrahedral elements by the Delaunay method, a three-dimensional meshcomposed of tetrahedral elements is created for the super tetra.Consequently, as shown in FIG. 3( c), on the boundary surface, atetrahedral element TA composed of nodes P1, P2, P4 and P5 and atetrahedral element TB composed of nodes P2, P3, P4 and P5 (or atetrahedral element TA composed of nodes P1, P2, P3 and P5 and atetrahedral element TB composed of nodes P1, P3, P4 and P5 (not shown))are generated. The tetrahedral element TA and tetrahedral element TB arecomposed of one common triangular element, and six triangular elementsthat are not shared by TA and TB.

Further, for the three-dimensional mesh composed of tetrahedral elementsgenerated by performing mesh division by the Delaunay method, meshdivision is performed again by the Delaunay method based on the nodes ofthe rotor. At this time, mesh division is performed so as not to erodethe above-mentioned triangular elements constituting the tetrahedralelements TA and the tetrahedral elements TB. A decision is made whetheror not the shape of the rotor-side portion is reproduced by the meshdivision. If a decision is made that the shape is not reproduced, a newnode is suitably added and mesh division is performed again by theDelaunay method. The addition of a node and the mesh division arerepeated until a decision is made that the shape is reproduced. Next,among the generated tetrahedral elements, unnecessary tetrahedralelements other than those of the rotor-side portion are deleted.Thereafter, as shown in FIG. 3( d), one quadrangular pyramid element isgenerated by joining the tetrahedral element TA and the tetrahedralelement TB. Similarly, by joining all tetrahedral elements constitutingthe periphery (boundary surface) of the spatial area two by two,quadrangular pyramid elements are generated. FIG. 4 is a perspectiveview showing the completed final three-dimensional mesh of therotor-side portion. FIG. 4( a) is a perspective view showing only therotor. FIG. 4( b) is a perspective view showing only the rotor rotatedby 90 degrees from FIG. 4( a). FIG. 4( c) is a perspective view showingthe rotor-side portion including the spatial area positioned inside theboundary surface, and FIG. 4( d) is a perspective view showing therotor-side portion rotated by 90 degrees from FIG. 4( c). On theboundary surface of the final three-dimensional mesh, the samerectangular elements as the rectangular elements of the initialthree-dimensional mesh shown in FIG. 2 are reproduced. Athree-dimensional mesh in which the whole rotor-side portion except theboundary surface is composed of tetrahedral elements is generated.

FIG. 5 is a flowchart explaining the processing steps performed by theCPU 11 of the three-dimensional mesh generator 1 of the presentinvention. First, the CPU 11 reads the initial three-dimensional meshdata of the rotor-side portion (step S1), and creates tetrahedralelements (super tetra) including the nodes of the rotor-side portion(step S2). For each of the rectangular elements constituting theboundary surface, the CPU 11 calculates the gravity of the rectangularelement (step S3), and creates a node P5 at an arbitrary distance h fromthe gravity calculated in step S3 to the rotor side in a normaldirection (step S4). For the super tetra created in step S2, meshdivision is performed based on the nodes (P1, P2, P3, and P4) on theboundary surface and the node P5 by the Delaunay method (step S5). For athree-dimensional mesh composed of tetrahedral elements generated instep S5, mesh division is performed again based on the nodes of therotor by the Delaunay method (step S6). Then, a decision is made whetheror not the shape of the rotor-side portion is reproduced (step S7). If adecision is made that the shape is not reproduced (step S7: NO), a newnode is added (step S8) and mesh division is performed again based onthe new node by the Delaunay method (step S9), and then the procedure isreturned to step S7. In step S7, if a decision is made that the shape ofthe rotor-side portion is reproduced (step S7: YES), unnecessarytetrahedral elements other than those of the rotor-side portion aredeleted (step S10), quadrangular pyramid elements are generated byjoining tetrahedral elements constituting the periphery (boundarysurface) of the spatial area two by two (step S11), and the procedure isfinished.

For the stator-side portion, by performing mesh division by theabove-described method, rectangular elements constituting the boundarysurface and tetrahedral elements constituting the stator-side portionare generated. When generating an initial three-dimensional mesh of thestator-side portion, by setting the number of divisions in dividing theboundary surface into rectangular elements at the same number ofdivisions on the boundary surface of the rotor-side portion,quadrangular pyramid elements whose base matches the base of thequadrangular pyramid elements constituting the boundary surface of therotor-side portion are generated on the boundary surface of thestator-side portion.

Although this embodiment illustrates a mode in which the boundarysurface is divided into rectangular elements in a grid form, the presentinvention is not limited to this mode, and it may be possible toimplement a mode in which the boundary surface is divided into suitablequadrilateral elements such as parallelograms. Moreover, although a modein which mesh division is performed for tetrahedral elements by theDelaunay method is illustrated, it may be possible to implement a modein which mesh division is performed by other dividing method such as anadvancing front method.

Next, the following description will explain the steps of a magneticfield analysis method for a rotating machine according to the presentinvention. Reference numeral 4 is a magnetic field analyzer for arotating machine of the present invention using a computer, whichcomprises: a CPU 41 for performing processing; a RAM 42; an externalmemory device 43 such as a CD-ROM drive; and an internal memory device44 such as a hard disk. By reading a computer program 50 of the presentinvention from a memory product 5 such as a CD-ROM of the presentinvention by the external memory device 43, storing the read computerprogram 50 into the internal memory device 44 and loading the computerprogram 50 into the RAM 42, the CPU 41 executes processes necessary forthe magnetic field analyzer 4 for a rotating machine, based on thecomputer program 50. The magnetic field analyzer 4 for a rotatingmachine comprises an input device 45 such as a keyboard or a mouse, andan output device 46 such as a liquid crystal display or a CRT display,and receives the user's operations such as input of data.

Moreover, the magnetic field analyzer 4 for a rotating machine maycomprise a communication interface 47, and may download the computerprogram 50 of the present invention from a server device 3 connected tothe communication interface 47 and execute processing by the CPU 41.

FIG. 7 is a flowchart explaining the processing steps performed by theCPU 41 of the magnetic field analyzer 4 for a rotating machine of thepresent invention. The CPU 41 generates a three-dimensional mesh of arotating machine to be analyzed by using the above-describedthree-dimensional mesh generation method (step S12), and rotates therotor-side portion by one step by shifting the rotor-side portion fromthe boundary surface by an amount of one element with respect to thestator-side portion (step S13). Next, the rotor-side portion and thestator-side portion are joined at the boundary surface (step S14), and amagnetic field analysis of the rotating machine is performed using afinite element method (step S15). Next, based on whether or not there isan instruction to finish the analysis from the user, the CPU 41 decideswhether or not to continue the analysis process (step S16). If the CPU41 decides to continue the analysis process (step S16: YES), theprocedure is returned to step S13. If the CPU 41 decides not to continuethe analysis process (step S16: NO), the procedure is finished.

Although this embodiment illustrates a mode in which the magnetic fieldanalyzer 4 for a rotating machine comprises means for generating athree-dimensional mesh, the present invention is not limited to thismode, and it may be possible to implement a mode in which the magneticfield analyzer 4 for a rotating machine does not comprise means forgenerating a three-dimensional mesh, and is constructed so that the dataof a three-dimensional mesh generated by the three-dimensional meshgenerator 1 is inputted to the magnetic field analyzer 4 for a rotatingmachine, and the magnetic field analyzer 4 for a rotating machineperforms a magnetic field analysis of the rotating machine by using theinputted the three-dimensional mesh data.

INDUSTRIAL APPLICABILITY

As described above, in the present invention, for the magnetic fieldanalysis of a rotating machine, when generating three-dimensional meshesof the stator-side portion and the rotor-side portion by setting aboundary surface in the spatial area between the stator and the rotor ofthe rotating machine, tetrahedral elements including nodes of each ofthe stator-side portion and the rotor-side portion are respectivelycreated based on quadrilateral element data constituting the boundarysurface divided by a suitable method, and polyhedral element orpolygonal element data constituting the stator-side portion and therotor-side portion excluding the boundary surface; a point is created atan arbitrary distance from the gravity of the quadrilateral element in anormal direction for each of the quadrilateral elements constituting theboundary surface; mesh division is performed for the tetrahedralelements based on the nodes on the boundary surface and the arbitrarypoint; and mesh division is further performed based on the nodesconstituting the stator and the rotor to generate the three-dimensionalmeshes of the stator-side portion and the rotor-side portion.Accordingly, even for a rotating machine whose shape is so complicatedthat a three-dimensional mesh cannot be generated by the conventionalthree-dimensional mesh generation method in which a two-dimensional meshis generated on a cross section perpendicular to the rotation axis ofthe rotating machine and a three-dimensional mesh is generated byextending the generated two-dimensional mesh in the rotation axisdirection, it is possible to generate three-dimensional meshes of thestator-side portion and the rotor-side portion respectively, and thus itis possible to generate the three-dimensional meshes of the stator-sideportion and the rotor-side portion for a magnetic field analysisregardless of the shape of the rotating machine.

Moreover, in the present invention, by performing mesh generation fortetrahedral elements including nodes of each of the stator-side portionand the rotor-side portion by the Delaunay method based on nodes, it ispossible to fully automatically divide the stator-side portion and therotor-side portion into tetrahedral elements to generate meshes.

Further, in the present invention, since the magnetic field analysis ofthe rotating machine is performed by the finite element method using thegenerated three-dimensional meshes, it is possible to perform accuratemagnetic field analysis in a shorter calculation time.

1. A three-dimensional mesh generation method for generatingthree-dimensional meshes of a rotating machine composed of a stator anda rotor to derive an output for analysis and display upon a computersystem, comprising steps of: setting a boundary surface in a spatialarea between the stator and the rotor to separate the rotating machineand the spatial area into a stator-side portion and a rotor-side portionand prescribing shapes of the stator-side portion and the rotor-sideportion; dividing the boundary surface into quadrilateral elements;dividing each of the stator-side portion and the rotor-side portion intotetrahedral elements including nodes; creating a point at an arbitrarydistance from a center of a gravity of the quadrilateral element to therotor side in a normal direction for each of the quadrilateral elementsconstituting the boundary surface and performing mesh division for thetetrahedral elements based on the point at the arbitrary distance andnodes on the boundary surface; and performing mesh division based onnodes of the stator and the rotor to generate three-dimensional meshesof the stator-side portion and the rotor-side portion.
 2. Thethree-dimensional mesh generation method as set forth in claim 1,wherein the mesh division is performed using the Delaunay method.
 3. Amethod of performing a magnetic field analysis of a rotating machine bya finite element method using a three-dimensional mesh of the rotatingmachine including a spatial area between a stator and a rotor, saidmethod comprising: generating a three-dimensional mesh of a rotatingmachine to be analyzed by using the three-dimensional mesh generationmethod defined in claim 1; and rotating the three-dimensional mesh ofthe rotor-side portion by shifting the elements from the boundarysurface, and performing a magnetic field analysis by the finite elementmethod.
 4. A method of performing a magnetic field analysis of arotating machine by a finite element method using a three-dimensionalmesh of the rotating machine including a spatial area between a statorand a rotor, said method comprising: generating a three-dimensional meshof a rotating machine to be analyzed by using the three-dimensional meshgeneration method defined in claim 2; and rotating the three-dimensionalmesh of the rotor-side portion by shifting the elements from theboundary surface, and performing a magnetic field analysis by the finiteelement method.